Optimal Stopping and the American Put

Optimal stopping and the American put under incomplete information

Optimal stopping is a sub-field of probability theory that is present within mathematical finance, mathematical statistics, stochastic calculus and other disciplines. In mathematical finance, one well known problem is the pricing of an American put option. In this thesis we first give a brief review of some general optimal stopping theory, its connection to free-boundary problems and we then ex...

Optimal stopping and American options

On the Optimal Exercise Boundary for an American Put Option

An American put option is a derivative financial instrument that gives its holder the right but not the obligation to sell an underlying security at a pre-determined price. American options may be exercised at any time prior to expiry at the discretion of the holder, and the decision as to whether or not to exercise leads to a free boundary problem. In this paper, we examine the behavior of the...

Randomization and the American Put

While American calls on non-dividend-paying stocks may be valued as European, there is no completely explicit exact solution for the values of American puts. We use a technique called randomization to value American puts and calls on dividend-paying stocks. This technique yields a new semiexplicit approximation for American option values in the Black-Scholes model. Numerical results indicate th...

Optimal Stopping and Applications Example 2: American options